Electrical resonators are widely incorporated in modern electronic devices. For example, in wireless communications devices, radio frequency (RF) and microwave frequency resonators are used as filters, such as ladder filters having electrically connected series and shunt resonators formed in a ladder structure. The filters may be included in a duplexer, for example, connected between a single antenna and a receiver and a transmitter for respectively filtering received and transmitted signals.
Various types of filters use mechanical resonators, such as bulk acoustic wave (BAW) resonators, including film bulk acoustic resonators (FBARs) and solidly mounted resonators (SMRs), or surface acoustic wave (SAW) resonators. The resonators generally convert electrical signals to mechanical signals or vibrations, and/or mechanical signals or vibrations to electrical signals. A BAW resonator, for example, is an acoustic device comprising a stack that generally includes a layer of piezoelectric material between two electrodes. Acoustic waves achieve resonance across the acoustic stack, with the resonant frequency of the waves being determined by the materials in the acoustic stack and the thickness of each layer (e.g., piezoelectric layer and electrode layers). One type of BAW resonator includes a piezoelectric film as the piezoelectric material, which may be referred to as an FBAR as noted above. FBARs resonate at GHz frequencies, and are thus relatively compact, having thicknesses on the order of microns and length and width dimensions of hundreds of microns.
Resonators may be used as band-pass filters with associated passbands providing ranges of frequencies permitted to pass through the filters. The passbands of the resonator filters tend to shift in response to environmental and operational factors, such as changes in temperature and/or incident power. For example, the passband of a resonator filter moves lower in frequency in response to rising temperature and higher incident power.